For clarification, I think the superscripts aren't powers but just a representation of the time-step, is this correct?

GKohavi

@knguyen0811 I think that's correct. For the most part I think this slide is saying that you can use velocity to estimate the change in position over some time and the same thing for velocity using acceleration.

moridin22

In particular, here we are using only the current velocity to estimate the change in position, and likewise for acceleration to estimate the change in velocity; this is part of why forward Euler is unstable.